Making a necklace with the curve modifier
Shrinkwrap modifier generates from curve tmp mesh. What you can see on your second image is original shape of your curve (shape without shrink-wrap modifier) I guess. It means your Curve modifier used by Torus still follows the original curve shape. What you see on your first image with shrinkwrap is actually a mesh :)
You have to convert curve to mesh (to get desired shape) than convert mesh back to curve.
Ensure if origins of Curve and Torus are at the same location.
Error message is probably referring to my first note - circle is still constructed from four points therefor applying modifier can't result in a shape presented by modifier that operates on mesh level. ... just my theory :)